Numerical solutions of random mean square Fisher-KPP models with advection
Corresponding Author
María Consuelo Casabán
Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Valencia, Spain
Correspondence
M. C. Casabán, Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain.
Email: [email protected]
Communicatedby: J. R. Torregrosa
Search for more papers by this authorRafael Company
Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Valencia, Spain
Search for more papers by this authorLucas Jódar
Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Valencia, Spain
Search for more papers by this authorCorresponding Author
María Consuelo Casabán
Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Valencia, Spain
Correspondence
M. C. Casabán, Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain.
Email: [email protected]
Communicatedby: J. R. Torregrosa
Search for more papers by this authorRafael Company
Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Valencia, Spain
Search for more papers by this authorLucas Jódar
Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Valencia, Spain
Search for more papers by this authorAbstract
This paper deals with the construction of numerical stable solutions of random mean square Fisher-Kolmogorov-Petrosky-Piskunov (Fisher-KPP) models with advection. The construction of the numerical scheme is performed in two stages. Firstly, a semidiscretization technique transforms the original continuous problem into a nonlinear inhomogeneous system of random differential equations. Then, by extending to the random framework, the ideas of the exponential time differencing method, a full vector discretization of the problem addresses to a random vector difference scheme. A sample approach of the random vector difference scheme, the use of properties of Metzler matrices and the logarithmic norm allow the proof of stability of the numerical solutions in the mean square sense. In spite of the computational complexity, the results are illustrated by comparing the results with a test problem where the exact solution is known.
CONFLICT OF INTEREST
The authors declare that there is no conflict of interests regarding the publication of this article.
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Citing Literature
Special Issue:Mathematical Modelling in Engineering & Human Behaviour 2018
30 September 2020
Pages 8015-8031
